Discussing important matters is best done face-to-face or at least over the phone. Text-based communication methods such as email and text messages are limited in expression, prone to misunderstandings and often lacking delivery guarantees.
I was having a discussion with another person over Facebook's chat and there was some visible lag in the way that his messages were popping up on my screen. At the end of the conversation, I had made a question but did not receive an answer before he quit, so I was puzzled. It had happened, that he indeed had written an answer and apparently it had showed up on his screen, but it had not reached the server and did not appear on my screen. Luckily it was possible to resolve the situation through text messages, but given the limitations of text messaging, not everything could be yet resolved (140 characters is not enough for everyone) and there was lots of room for misunderstandings (in his reply one word had two interpretations, although from the context it was possible to guess what it meant). A telephone call or a face-to-face discussion would have been needed.
Another case: There was an event where I should have been. One evening, a couple of days before the event, I received a text message from a friend asking whether I would be coming there. Knowing his habit of confirming things like this a couple of days beforehand, I replied "yes" without thinking anything special about it. But actually, the event had been moved to the beginning of the week and I had not heard about it, and now my friend was in reality asking, whether I would be there in 15 minutes because it was already starting. But his text message did not mention the time, that it was today, nor that the situation was urgent. So I was completely oblivious and missed the appointment that day. On the other hand, if he would have made a phone call, the reality would have become apparent from his tone of voice and the background noises. Then I could at least have said right away, that I won't be able to make it, and they could have prepared a Plan B.
What is wrong with text-based communication
The biggest problem with text-based communication is that it does not convey the tone of voice nor facial expressions. This makes it hard for the reader to interpret the intentions and motives of the writer correctly. It also makes it easier have arguments, especially when combined with relative anonymity. I can't even count how many misunderstandings and arguments I've seen happening over the internet during the last 10 years. It happens even to experienced people all the time.
High latency makes it easier to have misunderstandings. When speaking face-to-face or over the phone, the latency is zero. But when writing a message, it will take many seconds, minutes, hours or even days before the writer will receive a reply. This leads to people writing longer messages, so as to optimize the number of messages which need to be sent. But this has the negative effect of reducing the feedback per statement - the reply will give feedback about the message as a whole, but not about every statement, which in turn makes it possible for some of the statements to be misunderstood without anybody noticing.
And because many statements are made before receiving feedback about them, if there is a fundamental misunderstanding in the first statement of the message, the rest of the message only amplifies that misunderstanding because the rest of the message relies on the same false assumptions. For example if the writer criticizes the other person unwarrantably, then a long message will amplify the critique and the other person will get offended. But if he would speak just one statement and then get a reply that the critique is unwarranted, it would only be a small displeasure which could be solved quickly by apologizing, before the other person has time to get offended.
The overhead of writing hinders effective communication by reducing the amount of communication. When more effort is needed to communicate, then people try to reduce the amount of communication and they will use less words. This is especially true for text messages, which are very hard to write using a phone's number keys. Also if the cost of sending a message is non-zero, such as when sending a text message, people will try to send less messages both by reducing the number of words they use and by squeezing more information into one message. But using less words has the negative effect of reducing the amount of details in the communication, which in turn leads to communication which leaves out important things or makes the words subject to misinterpretation.
Still one more problem is unreliable delivery. Most of the communication mediums do not guarantee that the recipient of the message will receive and read it. Email messages can disappear into thin air, get caught in a spam filter, or take many days before arriving. If you're lucky, you will get an "Undelivered Mail Returned to Sender" message, but even that is not guaranteed. Text messages likewise can just disappear or take a long time to arrive. The email and text message infrastructures are fundamentally wrong, and there is no easy way to solve these problems with them.
Apparently also Facebook's chat does not guarantee delivery and gives the user misleading visual feedback. I haven't read the code, but it might be that when somebody sends a message, it is immediately processed on the client-side and shown in the chat log, after which the message update is sent asynchronously to the server. The right way would be to send the message first to the server and show the message in the chat log only after the server notifies the client about a new message. (If Facebook already uses the latter approach, then they must have some buggy code, because otherwise the issue I mentioned above would not have happened.)
How spoken communication avoids many of these issues
Just as it is said, "the most efficient and effective method of conveying information [--] is face-to-face conversation." Face-to-face communication is superior to other forms of communication. If face-to-face conversation is 90% effective, then phone calls would be maybe 50% effective, emails about 30% effective and text messages some 5% effective (statistics based on the Stetson-Harrison method).
When speaking face-to-face, it's possible to see from that person's facial expressions and tone of voice whether his intent was to give advice, to insult, to joke or something else. The words can be exactly the same, but the way they are said can completely change the meaning. But over the internet none of those cues exist, and people tend to misunderstand the writer's intent. Often the words come out very direct, even insulting. People are used to softening their words with their tone of voice and expressions, so in spoken communication the words don't come out that directly, but very few are so good writers that they can express the same softness and feeling in their writing.
When one person says something that the other person does not understand, the speaker can notice it in face-to-face discussion just by looking at the other person's facial expressions, and then he can refine his words and offer further explanation, and the misunderstanding will be fixed before it even happens. The same error-correction mechanism works also when speaking over the phone: a short pause, an interjection or a filled pause (uh, er, um) can signify that the other person did not understand something. It's also common for a person to repeat what the other said, so confirming that they have understood each other. Because spoken communication has little overhead, people are inclined to talk things through until all apparent issues have been solved.
In written communication these error-correction mechanisms don't exist. No facial expressions can be seen over the keyboard. It's not possible to detect half a second pauses in the other person's writing. People don't use filled pauses in their writing, because their use happens naturally without thinking, whereas written text always goes through some thinking (though rarely enough thinking). Because there is some overhead to writing, people are less inclined to making clarifying questions and repeating the other person's thoughts in their own words, to make sure that everything was understood correctly. Written communication removes such things as "unnecessary", which in turn leads to written communication being more error-prone.
The next time that you need to communicate something important, primarily try to say it face-to-face, secondarily make a phone call, tertiarily write a long email message or letter (it's easier to explain yourself through many words) and only as a last resort use a text message or other space-limited text-based means of communication.